On the isomorphism problem for Cayley graphs of abelian groups whose Sylow subgroups are elementary abelian or cyclic
type: Item
instance of: scholarly article
title: On the isomorphism problem for Cayley graphs of abelian groups whose Sylow subgroups are elementary abelian or cyclic
zbMATH Open document ID: 1391.05280
author: Ted Dobson
published in: The Electronic Journal of Combinatorics
publication date: 2018-06-27T00:00:00Z
full work available at URL: v25i2p49
review text: Summary: We show that if certain arithmetic conditions hold, then the Cayley isomorphism problem for abelian groups, all of whose Sylow subgroups are elementary abelian or cyclic, reduces to the Cayley isomorphism problem for its Sylow subgroups. This yields a large number of results concerning the Cayley isomorphism problem, perhaps the most interesting of which is the following: if \(p_1,\ldots, p_r\) are distinct primes satisfying certain arithmetic conditions, then two Cayley digraphs of \(\mathbb{Z}_{p_1}^{a_1}\times\cdots\times\mathbb{Z}_{p_r}^{a_r}\), \(a_i\leq 5\), are isomorphic if and only if they are isomorphic by a group automorphism of \(\mathbb{Z}_{p_1}^{a_1}\times\cdots\times\mathbb{Z}_{p_r}^{a_r}\). ~That is, that such groups are CI-groups with respect to digraphs.
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 6895332
zbMATH Keywords: Cayley graph
zbMATH Keywords: CI-group
zbMATH Keywords: isomorphism
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6895332